Method of Extending Hyperfine Coherence Times in ${\mathrm{P}\mathrm{r}}^{3+}:{\mathrm{Y}}_2{\mathrm{S}\mathrm{i}\mathrm{O}}_5$

In this Letter, we present a method for increasing the coherence time of praseodymium hyperfine ground state transitions in ${\mathrm{P}\mathrm{r}}^{3+}:{\mathrm{Y}}_2{\mathrm{S}\mathrm{i}\mathrm{O}}_5$ by the application of a specific external magnetic field. The magnitude and angle of the external field is applied such that the Zeeman splitting of a hyperfine transition is at a critical point in three dimensions, making the first order Zeeman shift vanishingly small for the transition. This reduces the influence of the magnetic interactions between the praseodymium ions and the spins in the host lattice on the transition frequency. Using this method a phase memory time of 82 ms was observed, a value 2 orders of magnitude greater than previously reported. It is shown that the residual dephasing is amenable to quantum error correction.

Figure 1

Two and three pulse echo sequences. $\pi$ pulse duration was $40\mu \mathrm{s}$ and the laser was turned off $150\mu \mathrm{s}$ before the pulse sequence and turned on $100\mu \mathrm{s}$ before the echo.

Figure 2

Spectrum of hyperfine transitions showing experimentally measured points as the magnetic field is applied in the $x$ direction, confirming the Hamiltonian used to model the system. Site 1a transitions are solid lines while site 1b are dashed lines. The transition used to investigate the critical point is bold. While the critical point investigated is not shown here, since it requires fields in the $y$ and $z$ directions, the behavior of the system exploited by the concept is clearly visible.

Figure 3

Two pulse echo sequences taken at the critical point magnetic field ${\mathit{B}}_{\mathrm{C}\mathrm{P}}=\{732,173,-219\}\mathrm{G}$ for transition $m_I=+1/2\leftrightarrow +3/2$ at site 1a (+). The $m_I=+1/2\leftrightarrow +3/2$ site 1b transition (×); the $m_I=-3/2\leftrightarrow +3/2$ transition (○) and the low field (0.5 G) $T_2=500\mu \mathrm{s}$ decay line shown for comparison.

Figure 4

Three pulse echo sequences taken at (a) $m_I=+1/2\leftrightarrow +3/2$ transition at site 1a (+) and site 1b (□), $m_I=-3/2\leftrightarrow +3/2$ transition (○); both traces were taken with ${\tau }_1=2.5\mathrm{m}\mathrm{s}$. The delay ${\tau }_2$ is measured on the $x$ axis, (b) critical point on transition $m_I=+1/2\leftrightarrow +3/2$ at site 1a. The ${\tau }_1$ delay for each echo sequence is labeled on the fit line.